@Khahan Unfortunately probability is rarely intuitive.
The mathematical proof:
We consider 3 type of card a, b, c and a deck with Na + Nb + Nc = 60 copies of each card.
The probably of having exactly A + B + C = 7 in a hand of 7 is given by
P(A, B, C; 60) = comb(Na, A) * comb(Nb, B) * comb(Nc, C) / comb(60, 7)
By introducing comb(60 - Na, 7 - A) in the middle we obtain
P(A, B, C; 60) = [comb(Na, A) * comb(60 - Na, 7 - A) / comb(60, 7)] * [comb(Nb, B) * comb(Nc, C) / comb(60 - Na, 7 - A)]
We recognize the probability for 2 type of card and use C = 7 - A - B to obtain
P(A, B, 7 - A - B; 60) = P(A, 7 - A; 60) * P(B, 7 - A - B, 60 - A)
Wikipedia for more detail.
The interpretation is: For each new type of card you have to remove the all the copy of the previous type of card.
This is not easy, I had to redo the proof to convince myself there was an error in the spreadsheet.
@ChubbyRain Nice work.
I think there is a error in "Chance of Green card out of the remaining six cards", your results correspond to a population of 59 = (60 - 1 * Force) but it should be done with population of 56 = (60 - 4 * Force).
Everything else seems good for me.
The number of set (with at least one new card) by year:
The number of new printing by year:
The year 2019 is ongoing so the number are incomplete.
There seem to have an increase in the number of new printing in the last few years.
@Shopsaholic It will be hard to hit four Karns with The Elderspell when there is only three versions of legendary Karn planewalkers.
The probme is that paying BB to destroy planewalkers when most of them cost 3 or 4 and have already use at least one of their abilities is a bit slow. And when they do not play planewalker, its a completely dead card.
The solution is to play Karn first.
My point is, it is better to play null rod than Harsh mentor, and Karn than Haunting Wind.
Well the premise here is that people are likely to have a turn 1 Karn, turn 2 time vault lock.
So you can only deploy 1 mana ?
Force of will, Mental misstep on key, Pithing needle, Nature claim, Lighting bolt.
And soon Force of Negation and Force of Vigor.